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Re: SV: st: Survey - raking - calibration - post stratification - calculating weights


From   Steven Samuels <sjhsamuels@earthlink.net>
To   statalist@hsphsun2.harvard.edu
Subject   Re: SV: st: Survey - raking - calibration - post stratification - calculating weights
Date   Sun, 7 Dec 2008 00:43:08 -0500

--

Stas, I am envious of statisticians who draw samples from those lists. This is a double sample and I agree with your advice: give everyone the weight for their age stratum:
                          weight1 = N_i/n_i
where "N" denotes population and "n" denotes sample size. Kristian apparently thinks of the 5,000 person sample as his "population"; the figure that he linked to does not show the initial sampling step at all. He may not have access to the one-year census counts. If he does not, I suggest that he use the N's from the 5,000. I suggest below that he also form geographic categories and rake those, with population counts, if possible, otherwise with counts from the 5,000. I roughly calculate that with 5,000 in the first phase sample, bias in estimates and in standard errors will be small.

Kristian, here is how to simultaneously match the age distribution and the geographic distribution of the final sample to your population. (This is called "sample balancing" or "raking".) Form age groups (agegp) and geographical groupings (geogp) and get the population counts(or percentages, see below) in each cell.

**************************CODE BEGINS**************************
* tot_agep =  total for population in participant age group (agegp)
* tot_geogp = total for population in participant geographical group (geogp)
**************************************************************

survwgt rake  weight1  ///
      by(agegp geogp) ///
      totvars(tot_agegp tot_geogp ///
      gen(weight2)
***************************CODE ENDS***************************


Raking can present problems, so so I suggest that you read http:// www.abtassociates.com/ presentations/raking_survey_data_2_JOS.pdf. If you cannot get population counts, perhaps you can get population percentages, multiply by 10 or 100 and round to the nearest whole number (e.g. 5.12% = 51 or 512), so that the population "size" is 1,000 or 10,000. For estimating means and proportions, these will yield nearly the same results as actual population counts. The Denmark census counts or percentages might be available only in larger age categories than the ones you used to draw the sample: say (60-64, 65-70,70-74). If so, use those for the raking calculations.

If you have, say, four geographical categories, you may be tempted to use 4 x 15 =60 stratification combinations. However, with only 600 people in the final sample, the numbers in individual cells will be too small for reliable estimation.

Theory for double sampling can be found in WG Cochran, 1973, Sampling Techniques, pp 117-119, 327-334, or in most other texts. Unfortunately, raking will not completely solve the problem of non- response.

-Steven

On Dec 6, 2008, at 11:19 PM, Stas Kolenikov wrote:

Steven,

you might be shocked, but people in Nordic countries do have their
population completely enumerated. Putting NJC's hat on :)), let me
remind you that this is an international list, and different countries
have different standards of how they collect and store their official
data. Denmark has a register with an equivalent of SSN that makes it
possible to combine the data three ways from economic, medical and
social perspectives. That's a survey statistician and a
microeconometrician dream... and they actually do have the capacity of
drawing SRS. That is, the first 5000 were SRS of the population, and
then Kristian continued a with stratified second phase sampling.

I would probably just give everybody the weight = # in age group
across Denmark (in some meaningfully defined period of the study) / #
in age in group in the sample. If you treat sample groups as
non-response adjustment cells, that's what this will probably boil
down to after multiplication of three or so fractions.
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